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Loren,

Looking at it from a programming POV, a standard compiler will evaluate the expression from the inside out, yielding the "real" answer (8). However, a good optimizing compiler will recognize that the two costly exponentiation operators can be combined into one. Such a compiler would presumably (I haven't tested this) produce the "imaginary" answer (-8i), or it might choke on taking a fractional power of a negative number.

The standards of most programming languages, including Fortran and C/C++, explicitly forbid optimizations that fail to preserve the integrity of parentheses in order to give programmers control of the sequence of operations when it matters. Thus, such an optimization is illegal.

Norm.
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